Deputy Leader of Fine Gael Simon Coveney has said he will not seek the party leadership in the wake of Leo Varadkar's resignation.
Mr Coveney said he made a "decision quite some time ago that he wouldn't stand in another leadership contest."
Speaking on RTÉ's Six One, the Minister for Enterprise, Trade and Employment said: "I had my chance and wasn't successful the last time, I think there's a lot of talent in the party.
"But look, I don't think we should be focusing on that today, I think we should focus on the role that Leo Varadkar has played in public life in Ireland, which is significant."
Leo Varadkar has said he believes the Coalition Government can be re-elected, and that his successor as Taoiseach would have up to a year before the next General Election.
Mr Varadkar made the comments as he made the surprise announcement that he is to stand down as Fine Gael Leader and he will leave the office of Taoiseach when the Dáil returns after the Easter break.
A new Fine Gael Leader will be in place by the Fine Gael Ard Fheis on Saturday 6 April.
Meanwhile, Fine Gael TDs and senators have been paying tribute to Taoiseach Leo Varadkar at their parliamentary party meeting tonight at Leinster House.
Mr Varadkar said there was no perfect or easy time for today's announcement.
He also thanked all colleagues for their loyalty and support, especially through testing and difficult times.
The Taoiseach said there is now an opportunity for the next leader and party and contended Fine Gael can have good European and local elections.
He also said he believed they could also regain more Dáil seats at the next General Election.
Mr Varadkar added that the next leader of Fine Gael will have his unequivocal support.
Earlier this evening, Mr Varadkar also ruled himself out of seeking to become an EU Commissioner.
He told journalists "it's not for me", although the post was always expected to be filled by a Fianna Fáil nominee.
Mr Varadkar said he will remain a Fine Gael TD for Dublin West and has not yet decided if he will run in the next General Election.
Speaking at Leinster House this morning, Mr Varadkar said that being Taoiseach has been the most fulfilling time of his life, with Ireland becoming a more equal and modern place, including for women and LGBT people.
Mr Varadkar explained that he is resigning as Fine Gael leader now and will remain as Taoiseach until a new party leader is elected after the Easter recess.
His successor will have a full two months before the local and European elections in June, he said.
"My reasons for stepping down are both personal and political ... I believe the re-election of this three party Government will be the right thing for the future of our country," he added.
"After careful consideration, and some soul searching, I believe a new Taoiseach will be better placed than me to achieve that.
He added that "after seven years in office, I don't feel I'm the best person for that job anymore".
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The Cabinet had been meeting in Government Buildings in advance of the announcement.
This morning there had been intense speculation about the Taoiseach's future.
The Government parties say that they do not expect today's announcement to trigger a general election.
First elected in 2007, the now 45-year-old Mr Varadkar has previously said he would not stay in politics beyond the age of 50.
In 2011, Mr Varadkar was appointed as minister for transport by then-taoiseach Enda Kenny, before taking up the health portfolio in 2014.
He became Taoiseach in 2017, after beating Simon Coveney in the race to succeed Mr Kenny. He was the youngest person to hold the post.
Following the 2020 general election, and the onset of the Covid-19 pandemic, a coalition agreement was reached between Fine Gael, Fianna Fáil and the Green Party.
That agreement saw Fianna Fáil's Micheál Martin become Taoiseach, with Mr Varadkar in the role of Tánaiste.
These roles were reversed in December 2022, with Mr Varadkar returning as Taoiseach for a second time as part of a deal with the coalition.
The announcement has caught many of his party colleagues by surprise.
It is anticipated that a Fine Gael leadership contest will now get under way.
The stability of the coalition Government is not thought to be in question at this point.
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Varadkar welcomed Stormont return in resignation announcement
Mr Varadkar's time in office coincided with two separate periods of Stormont collapse which amounted to five years where devolution was in cold storage.
The first was when Sinn Féin withdrew in 2017 for three years and then again in 2022 when it was the DUP that pulled the plug.
He cited the fact that the institutions of the Good Friday Agreement were back up and running as one of the reasons why it was as "good a time as any" to step down.
Much of Mr Varadkar's efforts in that time were concentrated on trying to navigate a route to the re-establishment of power-sharing through the choppy waters of Brexit.
Also in town was the British Prime Minister Rishi Sunak, but it was a somewhat surreal experience.
Both were in Belfast at the same time for the same occasion, but it certainly could not have been described as a joint visit.
There was a feeling in British circles that Mr Varadkar had inserted himself into a day that rightly belonged to their man.
But the Fine Gael leader’s efforts to right the ship of devolution were appreciated in many circles.
SDLP leader Colum Eastwood said he always found him to be "direct, supportive and willing to do whatever he could to support the political process in the North".
He had been a "relentless ally", Mr Eastwood said.
Unionists had a more jaundiced view.
They blamed him for Irish Sea border checks accusing him of raising the potential of a return of violence if they were to be established along the 300 mile land border between North and South.
They also did not welcome his talk about the possibility of a united Ireland in his lifetime and the need for a Plan B if the political institutions at Stormont could not be restored.
There was a muted response in unionist circles to the news that he was going. The only immediate public comment was from Ulster Unionist leader Doug Beattie who acknowledged it had come as a surprise.
He wished Mr Varadkar well, adding: "We look forward to working with his successor in a constructive manner, fostering good relationships."
Additional reporting Paul Cunningham, Conor Macauley
